I do a little vocal demo work. Typically I will rehearse the song so I know it and then I will lay down four or five lead vocal tracks. I usually use the last or second to the last one because I've gotten rolling by then. Maybe 45% of the time I use the track I select without punch-ins or comps. Maybe 50% of the time I will use another one of the tracks to comp in a phrase or two that I may have delivered a little better. Probably not necessary in most cases, but I try to deliver the best track I can. The rest of the time I may do a little more surgery but if it gets too bad I'll just re-track it the next day. Hey, it happens...
BG vocals, I usually do a little warm up and take first takes of them. I just did one last night where I layered 7 BG vocal tracks (2 harmony parts). No comps or punch ins. I did waste 3 tracks warming up though

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I guess you do what works best. If you are pitchy, keep doing it until you get it right or have enough tracks to comp a good one. I have pretty good pitch but every once in a while I get a client who either has better ears than I do or just is obsessive about pitch (funny thing is usually they can't sing worth a lick themselves

). What I have found in some cases is there are times being SLIGHTLY pitchy works. Like little slides up to notes etc. This gives the vocal a feel or a style. If you analyze an Elvis vocal track with autotune I bet he'd be off a fair amount quite a bit. But it works. I think exact pitch on every note would make quite a sterile sound. Now I'm not talking about sounding like two cats fighting in a burlap bag pitch issues. I'm talking about very minor (unnoticeable to most) variations.